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64 International Journal of Grid and High Performance Computing, 6(1), 63-76, January-March 2014
the dynamic change of numeric energy efficien-
cy factors (such as energy cost, carbon emission
rate, workload, and CPU power efficiency)
across different data centers depending on their
locations, architectural designs, and manage-
ment systems. Beloglazov et al. (Beloglazov
& Buyya, 2010) proposed an energy efficient
resource management scheme for virtualized
cloud data centers that reduces operational
cost while providing the required Quality of
Service (QoS). In this scheme, energy savings
are achieved by continuous consolidation of
VMs according to current resource utilization,
virtual network topologies between VMs, and
thermal states of computing nodes. Rodero
et al. (Rodero, Jaramillo, Quiroz, Parashar &
Guim, 2010) presented an energy-aware online
provisioning approach for HPC applications
on consolidated and virtualized computing
platforms. Energy efficiency is achieved by
using a workload-aware, just-right dynamic
provisioning mechanism with an assumption
of the ability to power off subsystems of a
host system that are not required by the VMs
mapped to it. Abdelsalam et al. (Abdelsalam,
Maly, & Kaminsky, 2009) created a mathemati-
cal model for power management of a cloud
computing environment that primarily serves
clients with interactive applications such as
web services. The mathematical model com-
putes the optimal number of servers and the
frequencies at which they should run. In the
literature (Younge, Laszewski, & Wang, 2010)
a new framework of a scalable cloud computing
architecture was presented. In this framework,
power-aware scheduling techniques, variable
resource management, live migration, and a
minimal virtual machine design are utilized
to improve the overall system efficiency with
minimal overhead. Chang et al. (Chang, Ren,
& Viswanathan, 2010) studied the optimal
resource allocation problem in clouds by for-
mulating demand for computing power and
other resources as a resource allocation with
multiplicity. They proposed an algorithm with
an approximation bound that can yield near
optimal solutions in polynomial time.
However, all of these current approaches
assumed the homogeneity of physical resources,
i.e., all nodes have the same characteristics
such as CPU speed, disk, memory, etc. In ad-
dition, most of these approaches considered the
processor as the only resource that contributes
to the energy consumption, leaving out other
important system resources such as memory
and disk storage. Sometimes, due to the massive
aggregation of workloads in the same node, the
present of bottle-necks in these other system
resources may reduce the performance of the
applications and increase the energy consump-
tion as mentioned in the literature (Lee, &
Zomaya, 2012).
The ability to reallocate VMs in run-time
enables dynamic consolidation of the workload
to reduce the energy consumption, as VMs can
be moved to a minimal number of physical nodes
and idle nodes can be switched to power saving
modes. However, VM migration leads to time
delays, performance overhead and extra power
consumption, requiring careful analysis and in-
telligent techniques to eliminate non-productive
migrations that can occur due to the workload
variation (Beloglazov & Buyya, 2011). Several
approaches have been proposed to reallocate
VMs to achieve optimal energy consumption
in cloud data centers. These approaches usually
model the problem as a bin packing problem
with a goal of minimizing the number of physi-
cal machines (PMs) employed. Bin packing is
a well-known combinatorial NP-hard problem.
Many heuristics and greedy algorithms have
been proposed for this problem (Karmarkar,
& Karp, 1982; Batu, & White, 1999). Heu-
ristics algorithms such as first-fit decreasing
(FFD) (Ferreto, Netto & et al., 2011), best-fit
decreasing (BFD) (Ferreto, Netto et al., 2011)
and Modified Best Fit Decreasing (MBFD)
(Beloglazov, Abawajy & Buyya, 2012) have
been used for VM allocation in Virtualized Data
Centers. However, minimizing the number of
PMs may not necessarily minimize the energy
consumption in a heterogeneous cloud environ-
ment due to the heterogeneity of the physical
machines. To address the problem, this paper
models the resource allocation problem in a
heterogeneous cloud data center as a constraint
satisfaction problem (CSP) (Haralick & Elliott,
1980). By solving this constraint satisfaction
